Market fraction hypothesis: A proposed test

Abstract

This paper presents and formalizes the Market Fraction Hypothesis (MFH), and also tests it under empirical datasets. The MFH states that the fraction of the different types of trading strategies that exist in a financial market changes (swings) over time. However, while such swinging has been observed in several agent-based financial models, a common assumption of these models is that the trading strategy types are static and pre-specified. In addition, although the above swinging observation has been made in the past, it has never been formalized into a concrete hypothesis. In this paper, we formalize the MFH by presenting its main constituents. Formalizing the MFH is very important, since it has not happened before and because it allows us to formulate tests that examine the plausibility of this hypothesis. Testing the hypothesis is also important, because it can give us valuable information about the dynamics of the market's microstructure. Our testing methodology follows a novel approach, where the trading strategies are neither static, nor pre-specified, as in the case in the traditional agent-based financial model literature. In order to do this, we use a new agent-based financial model which employs genetic programming as a rule-inference engine, and self-organizing maps as a clustering machine. We then run tests under 10 international markets and find that some parts of the hypothesis are not well-supported by the data. In fact, we find that while the swinging feature can be observed, it only happens among a few strategy types. Thus, even if many strategy types exist in a market, only a few of them can attract a high number of traders for long periods of time.

Introduction

In the agent-based financial literature, the proportion of different types of trading strategies in a market can be referred to as the Market Fraction. A common observation in many agent-based financial models is that the market fraction of the trading strategy types that exist in a market keeps swinging (i.e., changing). In other words, if for instance we have two types of agents in the market (e.g., fundamentalists and chartists), it has been found that the fraction of these two types of strategies keeps changing over time. If, for example at time t 90% of the market participants adopt the fundamental strategy and 10% of them adopt the chartist strategy, these fractions change continuously over time; therefore, in a future time period, we could observe that the fundamentalists occupy only 10% of the agents, and the chartists the other 90%. This swinging feature has been observed in many agent-based financial models (Amilon, 2008, Boswijk et al., 2007, Brock and Hommes, 1998, Gilli and Winker, 2003, Kirman, 1991, Kirman, 1993, Lux, 1995, Lux, 1997, Lux, 1998, Winker and Gilli, 2001).

Based on these observations about the swinging of the market fraction, Chen (2008) and Chen, Chang, and Du (2012) suggested a new hypothesis, called the Market Fraction Hypothesis (MFH). The MFH states that there is a constant swinging among the fractions of the types of trading strategies that exist in a market. However, although the term ‘Market Fraction Hypothesis’ was introduced and used by Chen, it has never been formalized as a hypothesis. This thus motivates us to formalize the MFH, by presenting its main constituents. Formalizing the hypothesis is very important, because it allows us to suggest and formulate tests that will examine its plausibility.

Furthermore, as we mentioned, the swinging feature that the MFH describes has been observed in several agent-based models. However, all of the above models assume that the trading strategy types are static and pre-specified. By this we mean that these models endow their agents with a specific number of trading strategy types which they have to choose from. To the best of our knowledge, the MFH has not been empirically examined under a more dynamic environment in which strategies are not static and are not exogenously given. Therefore, in this paper we will present a new agent-based financial model which incorporates this more general setting and test it.

In addition, motivated by the fact that the observations about the swinging of the market fraction have so far only taken place under artificial frameworks (Chen et al., 2012), we test the MFH under empirical datasets. We run tests for 10 international markets and hence provide a general examination of the plausibility of the MFH. One goal of our empirical study is to use the MFH as a benchmark and examine how well it describes the empirical results which we observe from various markets. In particular, we are interested in knowing how this benchmark performs when we tune the key parameter, i.e., the number of types in the market. More details regarding tuning the number of trading strategies can be found in Section 7.

Therefore, the objectives of this paper can be summarized in the following way: (i) formalizing the MFH, (ii) suggesting a new agent-based financial model which does not assume pre-fixed types of trading strategies, (iii) suggesting a testing methodology for the MFH, and (iv) testing the hypothesis under empirical datasets.

The remainder of this paper is organized as follows. Section 2 formalizes the MFH by presenting its main constituents. Section 3 then presents a brief overview of the different types of agent-based financial models that exist in the literature, and also discusses their limitations. In order to address these limitations, we have created a new agent-based financial model, which is presented in Section 4. In addition, Section 4 presents the two techniques that our agent-based model uses, namely, Genetic Programming (GP) (Koza, 1992, Poli et al., 2008) and Self-Organizing Maps (SOM) (Kohonen, 1982). Furthermore, Section 5 presents the experimental designs. Section 6 addresses the methodology employed to test the MFH and explains the technical approaches needed to be taken to facilitate the testing of the MFH. Section 7 presents the test results. It first starts by presenting the results over a single run for a single dataset. Then it continues by presenting the summary results over 10 runs for this dataset and it finally presents summary results for all datasets. Section 8 concludes this paper and briefly discusses possible directions for further research.